How do you find the asymptotes for #y= (x + 2) / ( x + 3)#?

Answer 1

vertical asymptote at x = - 3
horizontal asymptote at y = 1

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : x + 3 = 0 → x = -3 is the equation

Horizontal asymptotes occur as #lim_(x→±∞) f(x) → 0#

If the degree of the numerator and the degree of the denominator are equal , as the are here , both of degree 1 , then the equation can be found by taking the ratio of leading coefficients.

#rArr y = 1/1 = 1 " y = 1 is the equation "#

Here is the graph as an illustration. graph{(x+2)/(x+3) [-10, 10, -5, 5]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.